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A216419
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Odd powers that are not prime powers.
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1
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225, 441, 1089, 1225, 1521, 2025, 2601, 3025, 3249, 3375, 3969, 4225, 4761, 5625, 5929, 7225, 7569, 8281, 8649, 9025, 9261, 9801, 11025, 12321, 13225, 13689, 14161, 15129, 16641, 17689, 18225, 19881, 20449, 21025, 21609, 23409, 24025, 25281, 25921, 27225
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OFFSET
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1,1
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COMMENTS
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Also odd perfect powers having no primitive root (intersection of A075109 and A175594).
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LINKS
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FORMULA
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Sum_{n>=1} 1/a(n) = 1/2 + Sum_{k>=2} mu(k)*(1-zeta(k)*(2^k-1)/2^k) - Sum_{p prime} 1/(p*(p-1)) = 0.0158808884... - Amiram Eldar, Dec 21 2020
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EXAMPLE
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81 = 9^2 as well as 81 = 3^4, therefore 81 is not a term.
225 can be expressed so in one way as (3*5)^2, therefore 225 is a term.
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MATHEMATICA
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nn = 27500; lst = Union[Flatten[Table[n^i, {i, Prime[Range[PrimePi[Log[2, nn]]]]}, {n, 2, nn^(1/i)}]]]; Select[lst, OddQ[#] && ! IntegerQ@PrimitiveRoot[#] &] (* Most of the code is from T. D. Noe *)
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PROG
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(Magma) [n : n in [3..27225 by 2] | IsPower(n) and EulerPhi(n) ne CarmichaelLambda(n)]; // Arkadiusz Wesolowski, Nov 09 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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